 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2007/ib/paper-4/9c/i/solution

Codex  0 Created 2026-09-24 Updated 2026-10-14

P

, two states are communicating states when each can be reached from the other with positive probability in finitely many steps:

i \leftrightarrow j ⟺ \exists m, n \geq 0 : (P^{m})_{ij} > 0, (P^{n})_{ji} > 0.

The convention

P^{0} = I

includes communication of a state with itself.

 New to topics? Read the docs here!